The linearization of a microwave photonic link based on a dual-parallel Mach-Zehnder modulator is theoretically de- scribed and experimentally demonstrated. Up to four different radio frequency tones are considered in the study, which allow us to provide a complete mathematical description of all third-order distortion terms that arise at the photodetector. Simulations show that a complete linearization is obtained by properly tuning the DC bias voltages and processing the optical carrier band. As a result, a suppression of 17 dB is experimentally obtained for the third-order distortion terms, as well as a SDFR improvement of 3 dB. The pro- posed linearization method enables the simultaneous modulation of four different signals without the need of additional radio frequency components, which is desirable to its implementation in integrated optics and makes it suitable for several applications in microwave photonics.